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The count part came to me fast, just a counter array per room.
Clarify the requirements and constraints first, then propose a hybrid data structure that combines a hash map for O(1) room counts and a balanced BST or heap for efficient top-K queries. Discuss trade-offs between update and query costs, and consider whether the movement pattern allows optimizations like lazy updates or bucketing.
Pro tip: Mention that in real-world systems, you'd often use a combination of a hash map and a sorted container like a skip list or a Fenwick tree to balance update and query costs, and discuss how you'd handle concurrent updates if needed.
Ask about the frequency of count vs. topKFastest operations, whether movements are monotonic (people only move forward), and if there are any memory constraints. This helps determine the optimal data structure.
Propose a hash map (roomId -> count) for O(1) count queries, and a balanced BST or max-heap keyed by distance moved, with ties broken by arrival time, for topKFastest. Explain how to maintain both structures on each move.
Detail the time complexity for count (O(1)) and topKFastest (O(k log n) with BST or O(k log n) with heap). Discuss how updates affect these structures and whether lazy updates or bucketing could improve performance.
Address ties in distance and arrival time, and consider if people can move backward. Mention potential optimizations like maintaining a separate index for arrival times or using a Fenwick tree for prefix sums if needed.
Conclude with a summary of the proposed solution, its complexities, and how it would scale with n. Mention any alternative approaches and why the chosen one is preferable for the given constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.